## Equilibrium Constant Kp Definition

When a reaction is at equilibrium, the forward and reverse reaction rate are same. The concentration of the reactants and products stay constant at equilibrium, even though the forward and backward reactions are still occurring.

When one or more of the reactants or products are gas in any equilibrium reaction, the equilibrium constant can be expressed in terms of partial pressure. Equilibrium constant expression in terms of partial pressure is designated as K_{p}.

Equilibrium constant Kp is equal to the partial pressure of products divided by partial pressure of reactants and the partial pressure are raised with some power which is equal to the coefficient of the substance in balanced equation.

## Equilibrium constant expression in terms of partial pressures

Let us consider a general gas phase equilibrium reaction where a moles of A molecule reacts with b moles of B molecule to form c moles of C molecule and d moles of D molecule.

According to equilibrium law the equilibrium constant K_{p} can be written as

Here P_{A }, P_{B}, P_{C }and P_{D }are the partial pressure of gas A, B, C and D respectively. And K_{p }is equilibrium constant and subscript p refers to partial pressure. Partial pressures are expressed in atmosphere.

### The important points to be remembered to write the expression of K_{p}

- In equilibrium equations, even though the both sided arrows (⇌) are used we consider left sided elements as reactants and right sided elements as products.
- The products are on the top in the expression (the numerator).
- The reactants stays on the bottom (the denominator).
- The partial pressure of the products and reactants are always raised to the power which is equal to the numerical coefficient of the respective substance in the balanced chemical equation.
- For any heterogeneous system the partial pressure of pure solids and liquids are not included in the equilibrium constant expression.

## K_{p }in homogeneous gaseous equilibria

A homogeneous gaseous equilibrium is one in which all the reactants and products are in gas phase. A good example of homogeneous gaseous equilibrium is the formation of ammonia through the Haber Process.

The K_{p }expression for this equilibrium reaction is

## K_{p }in heterogeneous equilibria

A heterogeneous equilibrium is one where reactants and products are not in same phase. For heterogeneous equilibrium the partial pressure of pure solids and liquids are not included in the equilibrium constant expression. As for example the heating of calcium carbonate in a closed vessel to form calcium oxide and carbon dioxide.

Here only carbon dioxide is in gas phase. The equilibrium constant for this reaction (by excluding any terms for solid) is

## Relationship between K_{p} and K_{C}

Assuming that all the gases in equilibrium reaction obey the ideal gas equation, the partial pressure (p) of a gas is

PV = nRT

Divide both sides by V,

Here n/V is the molar concentration. Thus the partial pressures of individual gases A, B, C and D are:

**P _{A} = [A]RT; **

**P**

_{B}= [B]RT;**P**

_{C}= [C]RT;**P**

_{D}= [D]RTSubstituting these value in equilibrium constant expression equation 1, we have

** K**_{P}** = K _{C} (RT)^{(c+d)-(a+b)}**

** K**_{P}** = K _{C} (RT)^{∆n }**…………..(2)

where ∆n = (c+d) – (a+b), the difference in the sums of the coefficients for the gaseous products and reactants.

From the expression (2) it is clear that when ∆n=0, K_{p }= K_{c}.

## Summary

- Equilibrium constant Kp is equal to the partial pressure of products divided by partial pressure of reactants and the partial pressure are raised with some power which is equal to the coefficient of the substance in balanced equation.
- For any heterogeneous system the partial pressure of pure solids and liquids are not included in the equilibrium constant expression.
**K**_{P}**= K**_{C}(RT)^{∆n}

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